Yes a student can sometimes be suspended for something that happened outside the school especially if what the student did relates to the school.
Or if a student texts something bad on his or her phone outside school and then brings the phone into school and the school staff find out about it then the school can suspend the student from the school.
A school should not be able to suspend or punish students for something that happened off the school grounds but the schools can and do suspend some students for things that happened after school hours and off school grounds.
So be careful on what you do even after school hours off of school grounds and even if you were to do something bad such as on a field trip or other school outing that happened off the school grounds you can get suspended or expelled for those things as well.